A few minutes after boot up (maybe a bit longer) I receive a not so very nice email from the kernel telling me that irq16 has been disabled.
I do not notice any immediate issues when this occurs, but at some point down the line, maybe 12-24 hours later, the network interface will stop working - the system cannot communicate in or out. Restarting the network service has no affect, the only way I get the network working again is by rebooting.

Start with yum update as that's the original 7.7 kernel and there have been numerous updates since then. You can find 3.10.0-1062.18.1 in the updates repo and that will be selected if you just yum update but since 7.8 is imminent, you can also directly update to what will be 7.8 by enabling the CR repo and updating from that instead - yum --enablerepo=cr update should do that.

You can also look at the output from lspci -vv and see if any other devices are listed as using IRQ 16 that might have caused this. What you''re seeing is that some device raised an interrupt and the driver that is listed as using it was not expecting that to happen and ignored it. Since the only device listed as using it is a USB controller, any other device that says it's also using it in lspci -vv might be the culprit.